# Non-Abelian Majorana fermions in topological $s$-wave Fermi superfluids

## TL;DR

This paper analytically derives Majorana zero-modes in vortices of a 2D s-wave Fermi superfluid with spin-orbit coupling, showing their topological nature and non-Abelian statistics, which are relevant for quantum computation.

## Contribution

It provides an analytical solution for Majorana zero-modes in s-wave superfluids with spin-orbit coupling, highlighting their topological properties and non-Abelian statistics.

## Key findings

- Majorana zero-modes are localized in vortices of the superfluid.
- The zero-modes obey non-Abelian statistics.
- Energy splitting due to Majorana hybridisation is calculated.

## Abstract

By solving the Bogoliubov--De Gennes equations analytically, we derive the fermionic zero-modes satisfying the Majorana property that exist in vortices of a two-dimensional $s$-wave Fermi superfluid with spin-orbit coupling and Zeeman spin-splitting. The Majorana zero-mode becomes normalisable and exponentially localised to the vicinity of the vortex core when the superfluid is topologically non-trivial. We calculate the energy splitting due to Majorana hybridisation and identify that the $s$-wave Majorana vortices obey non-Abelian statistics.